In a large pot, heat the olive oil over medium heat.

Add the chopped onion and cook until translucent, about 5 minutes.

Stir in the minced garlic and chopped carrot, cooking for another 3-4 minutes until the carrot is softened.

Add the crushed tomatoes, vegetable broth, dried basil, and dried oregano. Season with salt and pepper to taste.

Bring the mixture to a boil, then reduce the heat and let it simmer for 20 minutes.

Using an immersion blender, blend the soup until smooth. Alternatively, you can transfer the soup to a blender in batches.

Stir in the heavy cream and heat through for an additional 5 minutes, but do not boil.

Serve the soup hot, garnished with fresh basil leaves.